Light Z′ and Dirac fermion dark matter in the B-L model

We consider a U ( 1 ) B - L model with a Z ′ portal Dirac fermion dark matter (DM) χ of low mass which couples very weakly to the B - L gauge boson Z ′ . An arbitrary B - L charge Q ≠ ± 1 , ± 3 of the DM χ ensures its stability. Motivated by the sensitivity reach of forthcoming “Lifetime Frontier” experiments, we focus on the Z ′ mass, m Z ′ , in the sub-GeV to few GeV range. To evaluate the DM relic abundance, we examine both the freeze-out and freeze-in DM scenarios. For the freeze-out scenario, we show that the observed DM abundance is reproduced near the Z ′ resonance, m χ ≃ m Z ′ / 2 , where m χ is the DM mass. For the freeze-in scenario, we focus on m χ ≪ m Z ′ . We show that for a fixed value of m Z ′ , g BL values roughly scale as 1/ Q to reproduce the observed DM abundance. For various Q values in the range between 10 - 6 and 10 2 , we show that the gauge coupling values g BL needed to reproduce the observed DM abundance lie in the search reach of future planned and/or proposed experiments such as FASER, Belle-II, LDMX, and SHiP. In the freeze-in case, the Q values to realize observable g BL values are found to be much smaller than that in the freeze-out case.